What is a Line Segment
By the end of this lesson, you will be able to
- define line segment in geometry.
- describe types of line segment.
- demonstrate examples of line segment.
- distinguish between line segment and line.
- compare open line segment and closed line segment.
- interpret half-open line segment.
Line Segment
A line segment, having two distinct end points, is a definite part of a line containing all the points between the endpoints.
Let's go to discuss the line segment definition geometry explicitly.
A line is shown in the figure above that doesn't have any endpoints.
Let A and B be the two distinct points on the line.
Cut the portion AB and isolate that is shown in the following figure.
That is the line segment AB.
A and B are two endpoints of line segment AB. And it also contains all the points between A and B.
Line Segment Example
Types of Line Segment
Generally, line segment is divided into the following parts:
- Closed line segment
- Open line segment
- Half-Open line segment
Closed line segment
A line segment is said to be a closed line segment if it contains both endpoints.
A line segment AB is shown in the figure.
A and B are two endpoints. The line segment AB contains all the points on AB including A and B.
Thus AB is a closed line segment.
It is denoted by [A,B]
Open line segment
A line segment is said to be open if it contains all the point on the line segment except both endpoints.
A line line segment AB is shown in the figure.
A and B are two endpoints. The line segment AB contains all the points on AB excluding both A and B.
Thus AB is a open line segment.
It is denoted by (A,B)
Half-Open line segment
A line segment is said to be half-open if it contains only one of the endpoints.
Line segment definition geometry includes two types of half-open line segment.
A line segment is shown in the followong figure.
This line segment contains all the points including end point B and excluding endpoint A.
That is; it contains only one of the endpoints.
Hence, it is a half-open line segment.
It is denoted by (A,B].
Again, a line segment is shown in the followong figure.
This line segment contains all the points including end point A and excluding endpoint B.
That is; it contains only one of the endpoints.
Hence, it is also a half-open line segment.
And it is denoted by [A,B).
